Geography Notes by Muhammad Kashif Aslam (33rd CTP PSP) - Page 2

Taimoor Gondal · #11 Tuesday, January 10, 2012

What is the necessity of drawing a map on some selected projection? What
Considerations are involved in the selection of the projection? Give examples.

MAP:

A map is a representation to scale of either the whole earth or a portion of it, on a plane-surface. Besides depicting various features of the earth, it has a network if the parallels of latitude and the meridians of longitude. The parallels and the meridians serve as co-ordinates for locating the absolute positions of the various points on the ground. They are known as geographic co-ordinates.

MAP PROJECTION:

A map projection is an orderly system of parallels and meridians used as a basis for drawing a map on a flat surface. The fundamental problem is to transfer the geographic grid from its actual spherical form to a flat surface in such a way as to present the earth’s surface or some part of it in the most advantageous way possible for the purpose desired. In other words, it is a method of representing the parallels and the meridians of the earth on a plane surface. The network of the parallels and the meridians so formed is called a graticule.

On our earth resembles a sphere. Therefore, a globe being spherical in shape represents the earth truly. Thus a globe is a true representation of the earth. In other words, a globe is true map of the earth. Since a map represents a flat surface and a globe a spherical surface, the shape of the network of the parallels and the meridians on a map is always different from that on a globe. There are a number of methods of transferring the parallels and the meridians of a globe on a plane surface, i.e., constructing map projections. The shape of the network of the parallels and meridians drawn by one method differs from that by the other methods. Therefore, there is a great variety of graticules. A variety in the graticules is necessary to meet various specific purposes.

Earth relationships such as shapes, areas of countries and direction of one place from the other, are not maintained on map. A map projection showing the area of a globe correctly will not maintain the shapes and directions of the areas truly. Thus it is not possible to construct a map projection showing the globe truly and there is always some distortion in the shape of the graticules. Being unable to acquire all the qualities of a globe, a map projection can’t be used as a complete substitute for a globe.

NECESSITY TO CONSTRUCT A MAP PROJECTION:

Earth is round and it resembles a sphere. Therefore, a globe which is also spherical in shape is a true representation of the earth and it gives three dimensional effect of the earth. Although size, shape and direction of an area are correctly represented on a globe, globe can’t be always used conveniently.

1. All the countries of the globe can’t be seen at a glance because only one half of the globe can be seen.

2. A globe is on too small a scale for many purposes. On globes ranging from a few inches to two or three feet in diameter, only the barest essentials of geography can be shown.

3. the few large globes in existence, those several feet in diameter, may show considerable detail, but they serve also to accentuate another shortcoming of globes—their lack of probability.

4. It is difficult to measure distances on a globe due to the spherical nature of its surface.

5. It is difficult to construct a large-sized globe and it is equally difficult to carry such a globe from place to place. It will be impossible for tourists, planners and army personnel to carry large-sized globes. The diameter of the globe on a scale of 1: 1,000,000 will be 14 yards (12.82 meters) and on a scale of 1:50,000 it will be 278 yards (254.6 meters).

6. It is not possible to trace maps from a globe accurately because a tracing paper on coming in contact with a globe develops many creases. In contrast maps on flat surfaces can be traced without any difficulty.

7. Even if a globe is split into various parts, it will not be convenient to carry and use them. A map on the other hand can be rolled and even folded and can thus be easily carried from place to place.

Flat maps are printed on paper can be folded compactly so that many may be carried in a small pocket, whereas even the smallest globe is a cumbersome and delicate object. Ease of reproduction greatly favors maps over globes. Making a quality globe requires not only that a map be printed but also that the map be trimmed and carefully pasted onto a spherical shell.

Thus the disadvantages of a globe are eliminated to some extent on map.

CHOICE OF PROJECTION:

When choosing a projection for a map the following points should be taken into consideration:

Special purposes for which the map is required.
Position of area as regards latitude.
Size of the map.

1. SPECIAL PURPOSE FOR WHICH THE MAP IS REQUIRED:

For statistical purposes i.e., for showing the distribution of rainfall, vegetation, products, minerals and population, etc., and for political maps such as those giving the extent of countries and administrative areas, equal-area projections are the best.

2. POSITION OF AREA AS REGARDS LATITUDE:

Considering position, if important areas lie in the equatorial latitudes the projection to be chosen should be one in which the distortion in these latitudes is the least. In case such a map extends much east and west, a cylindrical projection is the best, otherwise the (equatorial) zenithal projection may be quite suitable. For maps of areas in temperate latitudes a conical or a modified conical projection is most suitable, while for the Polar Regions a zenithal projection is the best.

3. SIZE OF THE MAP:

As regard size, maps can be divided into three broad classes:

World maps.
Atlas maps.
Survey maps.

i. WORLD MAPS:

World maps are the maps of the whole world or of a hemisphere in one sheet. They are on a very small scale.

The projection for a world map is chosen independently for the individual map, in consideration of the purpose in view

ii. ATLAS MAP:

Atlas maps are the maps of large portions of the earth such as those of the continents and countries. They are also on small scales.

The projection for an atlas map is selected with regards to the purpose in view as well the position in latitude and longitude

iii. SURVEY MAPS:

Survey maps are the maps of small areas. They are on large scale.

In survey maps the question of projection is not of great importance, as each sheet covers so small a portion that there is little difference between the merits of several projections and the representation is more or less perfect.

The choice may be guided by considerations of convenience and economy of time. In these maps it is desirable that the projection should be such that the adjacent sheets may fit with one another so that they may be combined to make larger map if necessary.

PROJECTION FOR DISTRIBUTION MAPS:

For a good distribution map the projection should be equal-area. The equal area projections for a map of the world are:
· cylindrical equal-area

the sinusoidal
the Mollweide.

EXAMPLES

Take an example in which projection is to be selected for showing the distribution of rice and wheat.

The chief rice-producing areas are either tropical or sub-tropical. So the projection to be selected should be one which represents these areas correctly and it matters little if the areas beyond them are distorted.

The cylindrical equal-area may, therefore, be selected as it is also easy to draw. As nearly all the wheat-producing countries lie in the temperate latitudes, the cylindrical equal-area will not be suitable to show their distribution and the choice will fall between the sinusoidal and the Mollweide, and the latter may be chosen because of its better representation of shape. In atlases generally the same protection is used for all the distribution maps; it seems to be simply for the sake of keeping uniformity.

For a map of the world to show the winds and the currents, the projection should be one in which the directions are correct and so the cylindrical orthomorphic or Mercator’s projection should be used. As this projection is employed in navigation charts to find a route between two places on a constants bearing which is represented by a straight line between them.

For a map of Hemisphere or any portion thereof, to find the shortest distances (or the shortest or great circle routes) between two places, the gnomonic projection is the best in which they would be represented by a straight line between them. So this projection is of great use in air transport where, undisturbed by topographical obstructions, shortest routes are likely to be followed.

For a map in which correct north and south distances are important (as for railway lines lying north and south), the projection to be selected should be one in which the meridian scale is correct, e.g., the simple cylindrical, the simple conical or the zenithal equidistant. Where east and west distances are important, the projection should have parallel scale to be correct. In this case any cylindrical projection will do well within a few degrees from the equator, but for higher latitudes a conical projection with one or two standard parallels will be suitable. Thus for a map of the east India railway and a small area on either side of it, the simple conical with two standard parallels will be quite suitable.

Taimoor Gondal · #12 Tuesday, January 10, 2012

12. Write explanatory notes on following:-
b. Map projection;

MAP PROJECTION:

A map projection is an orderly system of parallels and meridians used as a basis for drawing a map on a flat surface. The fundamental problem is to transfer the geographic grid from its actual spherical form to a flat surface in such a way as to present the earth’s surface or some part of it in the most advantageous way possible for the purpose desired. In other words, it is a method of representing the parallels and the meridians of the earth on a plane surface. The network of the parallels and the meridians so formed is called a graticule. A strip between two meridians iscalled a gore and that between two parallels a zone.

When the plane of a projection touches the globe at a pole, it is called normal (polar). If it touches any point on the equator, it is equatorial, while if it touches some point between the equator and the poles, it is oblique. When a plane of a projection turns through right angle, it is made transverse

On our earth resembles a sphere. Therefore, a globe being spherical in shape represents the earth truly. Thus a globe is a true representation of the earth. In other words, a globe is true map of the earth. Since a map represents a flat surface and a globe a spherical surface, the shape of the network of the parallels and the meridians on a map is always different from that on a globe. There are a number of methods of transferring the parallels and the meridians of a globe on a plane surface, i.e., constructing map projections. The shape of the network of the parallels and meridians drawn by one method differs from that by the other methods. Therefore, there is a great variety of graticules. A variety in the graticules is necessary to meet various specific purposes.

Earth relationships such as shapes, areas of countries and direction of one place from the other, are not maintained on map. A map projection showing the area of a globe correctly will not maintain the shapes and directions of the areas truly. Thus it is not possible to construct a map projection showing the globe truly and there is always some distortion in the shape of the graticules. Being unable to acquire all the qualities of a globe, a map projection can’t be used as a complete substitute for a globe.

NECESSITY TO CONSTRUCT A MAP PROJECTION:

Earth is round and it resembles a sphere. Therefore, a globe which is also spherical in shape is a true representation of the earth and it gives three dimensional effect of the earth. Although size, shape and direction of an area are correctly represented on a globe, globe can’t be always used conveniently.

1. All the countries of the globe can’t be seen at a glance because only one half of the globe can be seen.

2. A globe is on too small a scale for many purposes. On globes ranging from a few inches to two or three feet in diameter, only the barest essentials of geography can be shown.

3. the few large globes in existence, those several feet in diameter, may show considerable detail, but they serve also to accentuate another shortcoming of globes—their lack of probability.

4. It is difficult to measure distances on a globe due to the spherical nature of its surface.

5. It is difficult to construct a large-sized globe and it is equally difficult to carry such a globe from place to place. It will be impossible for tourists, planners and army personnel to carry large-sized globes. The diameter of the globe on a scale of 1: 1,000,000 will be 14 yards (12.82 meters) and on a scale of 1:50,000 it will be 278 yards (254.6 meters).

6. It is not possible to trace maps from a globe accurately because a tracing paper on coming in contact with a globe develops many creases. In contrast maps on flat surfaces can be traced without any difficulty.

7. Even if a globe is split into various parts, it will not be convenient to carry and use them. A map on the other hand can be rolled and even folded and can thus be easily carried from place to place.

Flat maps are printed on paper can be folded compactly so that many may be carried in a small pocket, whereas even the smallest globe is a cumbersome and delicate object. Ease of reproduction greatly favors maps over globes. Making a quality globe requires not only that a map be printed but also that the map be trimmed and carefully pasted onto a spherical shell.

Thus the disadvantages of a globe are eliminated to some extent on map.

DEVELOPABLE SURFACE:

A geometric form that makes a flat surface on unrolling is called a developable surface.

Certain geometric surfaces are said to be developable because by cutting along certain lines can be made to unroll or unfold to make a flat sheet.

FORMS OF DEVELOPABLE SURFACES:

Cylinder and cone are the two geometric forms that are developable. Were the earth conical or cylindrical, the map projection problem would be solved once and for all by using the developed surface. No distortion of surface shapes or areas would occur, although it is true that the surface shapes or areas would occur, although the surface would be cut apart along certain lines.

Let us have a cylinder made of thick paper and let it stand on a table. If we cut this cylinder vertically downwards, we can unroll it to make a flat sheet resembling a rectangle. Similarly if we cut a cone from its apex downwards, and unroll it, we get a flat sheet resembling a portion of circle. There shall not be any distortion in the shapes and any change in the areas on the flat sheets so developed. Evidently it would have been very easy to represent the earth on flat sheets had it resembled either a cylinder or a cone and we would have not needed to evolve methods of transferring the parallels and meridians of the reduced earth on a flat surface.

The globe which represents the earth correctly being spherical, i.e., three dimensional in shape, is not a developable geometric form. If we flatten a part of a globe, stretching must occur and that too in a non-uniform manner. Thus we need to develop methods to project a globe on a flat, i.e., two dimensional surfaces. The resultant map will not, however, represent the earth truly and it will have some shortcomings.

The earth belongs to a group of geometric forms said to be un-developable, because no matter how they are cut, they cannot be unrolled or unfolded straight line in one or more directions on the surface of a developable solid, but nowhere can this be done on an un-developable form such as a spherical surface. In order to make the parts of a spherical surface lie perfectly flat, it must be stretched—more in some places than in others. Thus it is impossible to make a perfect map projection.

When a map is made of a very small part of the earth’s surface—for example, an area of four miles across—the map-projection problem can be ignored. If the meridians and parallels are drawn as straight lines, intersecting at right angles and correctly spaced apart, the actual error present is probably so small as to fall within the width of the lines drawn and is not worth correcting. As the area included on the map is increased, however, the problem gains in importance. When attempt is made to show the whole globe, very serious trouble develops. Only some compromise can the distortion be reduced to a reasonable degree over important parts of the earth’s surface. Map projections actually improve our ability to perceive the earth’s surface

MAP SCALE:

All globes and maps depict the earth’s features in much smaller size than the true features that they attempt to represent. Globes are intended, in principle, to be perfect models of the earth itself, differing from the earth only in size, but not in shape. The scale of a globe is therefore the ratio between the size of the globe and the size of the earth, where size is expressed by some measure of length or distance (but not area or volume). Take, for example, a globe 10 inches in diameter representing the earth, whose diameter is about 8000 miles. The scale of the globe is therefore the ratio between 10 inches and 8000 miles. Dividing both figures by 10, this reduces to a sale stated as one inch represents 800 miles, a relationship that holds true for distances between any two points on the globe. (Stated in metric units, the scale of this globe would be ratio of 25cm to 12.900 km. or 1 cm. represents 516 km.).

Scale is more usefully stated as a simple fraction, termed the fractional scale, or representative fraction (RF), which can be obtained by reducing both map and globe distances to the same unit of measure. Thus:

1 inch on globe = 1 inch .
800 miles on earth 800 × 63,360 inch (per mile)

= 1 inch .
50,688,000 inch.

= 1 . .
50,688,000

This fraction may be written as 1:50,688,000 for convenience in printing. The advantage of representative fraction is that it is entirely free of any specified units of measure, such as the foot, mile, meter, or kilometer. Persons of any nationality understand the fraction regardless of the language or units of measure used in their nation, provided only that they use Arabic numerals.

SCALE OF GLOBE:

A globe is a true-scale model of the earth, in that the representative fraction applies any distances on the globe, regardless of the latitude or longitude, and regardless of the compass direction of the line whose distance is being considered curve surface of the sphere to conform to a flat plane, all map projections stretch the earth’s surface in a non uniform manner, so hat the fraction scale changes from place to place. Thus, this can’t be said about a map of the world that “the scale of this map is 1:50, 000, 000,” because the statement is false for any form of projection.

It is quite possible to have the fractional scale of a flat map remain true, or constant, in certain specified directions. For example, Polyconic projection preserves constant scale along all parallels, but not along the meridians. Azimuthal equidistant projection keeps scale constant along all meridians. The gnomonic projection has changing scale along both meridians and parallels.

RADIUS OF A GLOBE:

The radius of the earth is not same at all the points on the surface of the earth. For example, the equatorial radius of the earth is 6378.2064 km (3963.0 miles) and the polar radius is 6356.5838 km (3949.5 miles). If earth is considered as a perfect sphere its radius works out at 6370.9972 km (3958.5 miles).

Radius of the earth if it were a perfect sphere = 6370.9972 km or 637,099,720 cm or 635,000,000 cm. approximately.

A globe of 1 cm radius is 1/635,000,000th of the size of the earth. In other words, if the R.F. of a globe is 1/635,000,000 its radius is one cm. if the RF. Is 1/127,000,000, the radius of the globe is 5 cm and if the R.F is 1/80,000,000, the radius of the globe is (1/80,000,000) × 635,000,000 or 7.937 cm.

Radius of the earth if it were a perfect sphere = 3958.5 miles.

Or 250,810,560 inches

Or 250,000,000 inches approximately.

A globe of 1 inch radius is (1/250,000,000) th of the size of the earth. In other words if the R.F. of a globe is 1/250,000,000, its radius is 1 inch.

If the R.F is 1/125,000,000, the radius of the globe is 1/125,000,000 × 250,000,000 or 2 inches.

Thus radius of the globe is found out if its scale is known.

EQUAL-AREA PROJECTION:

A map projection is said to be equal-area or homolographic if areas of a country shown on it is equal to the area of the same country on the globe constructed on the scale on which the map projection has been drawn A projection, however, achieves the property of equal-area only at the cost of the shape of the area it shows. If the scale is large along the parallels, the scale along the meridians is reduced and vice versa. Thus there being a marked inequality between the scale along the parallels and that along the meridians, shapes of areas are deformed on the equal-area projections.

PRESERVING AREAS ON MAP PROJECTIONS:

Because a globe is a true-scale model of the earth, given areas of the earth’s surface are shown to correct relative scale everywhere over its surface. The scale of distance is constant in all compass directions. If we should take a small wire ring, say one inch in diameter, and place it anywhere on the surface of the ten-inch globe, the area enclosed will represent an equal amount of area of the earth’s surface. But a similar procedure would not enclose constant area on all parts of most map projections, only on those having the special property of being equal-area projections.

If no projection preserves a true or constant scale of distances in all directions over the projection, how can circles of equal diameter placed on the map enclose equal amounts of earth area? The answer is suggested in the figure.

The square, one mile on a side, encloses one square mile between two meridians and two parallels. The square can be deformed into rectangles of different shapes, but if the dimensions are changed in an inverse manner, each will still enclose one square mile. The scale has been changed in one direction to compensate for change in another in just the right way to preserve equal areas of map between corresponding parts of intersecting meridians and parallels. Hence, any small square or circle moved about over the map surface will enclose a piece of the map representing a constant quantity of area of the earth’s surface.

ORTHOMORPHIC PROJECTIONS:

An orthomorphic projection is also known as a conformal projection. It literally means ‘true shape’. In every orthomorphic projection:

1 The parallels and the meridians intersect each other at right angles

2 The scale along the meridians is also increased so that the scale along the parallels and the meridians is the same at a point.

Owing to these two important properties, a conformal map projection preserves shapers of small areas that is the shape of a very small country appears on the projection as it appears on the globe. The scale is, however, different n the different parts of the projection. The shapes of large areas are, therefore, not preserved on this projection

PRESERVING SHAPES ON MAP PROJECTIONS:

A map projection is said to be conformal, or orthomorphic, when any small piece of the earth’s surface has the same shape on the map as it does on a globe. Thus, the appearance of small islands or countries is faithfully preserved by a conformal map. One characteristic of a conformal projection is that parallels and meridians cross each other at right angles everywhere on the map, just as they do on the globe. However, not all projections whose parallels and meridians cross at right angles are conformal.

Another way of saying that parallels and meridians intersect at right angles is that shearing of areas doesn’t occur. For projections consisting of straight parallels and meridians, shearing gives parallelograms formed of acute and obtuse angles. For projections with curved meridians and parallels, straight lines are drawn tangent to the curves at the point of intersection. If these tangent lines cross at right angles, the projection is not sheared; but if the tangents form obtuse and acute angles, shearing is present. Conformal maps are not sheared but not all maps without shearing are conformal. A conformal map cannot have equal area properties besides, so that some areas are greatly enlarged at the expense of others. Generally maps have a much larger scale than central ones.

In all conformal projections the principle of construction prevents coverage of the entire globe within a single orientation of the projection. Instead, as totality of globe coverage is approached, dimensions of the map sheet needed to show totality approach infinity.
.
CLASSIFICATION OF MAP PROJECTIONS:

There are two ways of classifying map projections. The first is based on the principle involved in their mode of development and the second is based on the group or family to which they belong.

CLASSIFICATION BASED ON THE MODE OF THEIR DEVELOPMENT:

Under this scheme we have flowing map projections:

Perspective map projections
Non-perspective map projections
Conventional map projections

PERSPECTIVE MAP PROJECTIONS:

The word perspective in the usual sense means the art of representing solid objects on a flat surface in such a way as to give the same impression of relative distance, size, etc., as the objects themselves do when viewed from a certain point. Thus in a perspective map projection the parallels and the meridians of the globe are represented on a surface geometrically from a point

TYPES OF PERSPECTIVE PROJECTIONS:

Following are the perceptive projections:

ZENITHAL PERSPECTIVE PROJECTIONS:
1 Gnomonic projection.
2 Stereographic projection
3 Orthographic projection.

NON PERSPECTIVE MAP-PROJECTIONS:

The perspective projections being of limited use have been modified to develop useful properties. Being modified to a great extent they remain no longer geometrical and are, therefore, known as non-perspective projections. They are so modified as to acquire any one or more of the following useful properties:

Equal area
Orthomorphic
General-purpose.

The non-perspective map projections since meet a number of requirements are far more useful and, therefore, more important than the perceptive map projections.

TYPES OF PERSPECTIVE PROJECTIONS:

Following are the non-perspective projections:

CYLINDRICAL MAP PROJECTIONS:

1 Simple cylindrical projection
2 Cylindrical equal-area projection.
3 Mercator’s or cylindrical orthomorphic projection.

CONICAL MAP PROJECTIONS (NORMAL CASE)

1 Simple conical projection with one standard parallel.
2 Simple conical projection with two standard parallels.
3 Bonne’s projection.
4 Polyconic projection.
5 International projection.

ZENITHAL MAP PROJECTIONS:

1 Zenithal equidistant projection.
2 Zenithal equal-area projection.

CONEVNTIONAL PROJECTIONS:

These projections do not fall into the systems of cylindrical, conical and zenithal projections. In these projections, the parallels and the meridians are drawn arbitrarily so as to make the graticule of a projection more useful for specific purposes. They are drawn generally for showing the whole world.

TYPES OF CONVENTIONAL PROJECTIONS:

Following are the conventional projections:
1 Sanson-Flamsteed or Sinusoidal projection
2 Mollweide’s projection.

CLASSIFICATION BASED ON THE FAMILY OF THE PROJECTIONS:

They are

1 Cylindrical map projections
2 Conical map projections
3 Zenithal map projections
4 Conventional map projections

SELECTION OF MAP PROJECTION:

Whether a conformal or equal area projection is to be selected depends on what is to be shown.

An equal-area projection is drawn when comparison of areas is required. Since comparison of areas is necessary when the distribution of commodities is shown these projections are used mainly for showing the areal distribution of population, animals, area under forest, area under agricultural crops, etc.

For most general purposes, a conformal type is preferable because physical features most nearly resemble their true shape on the globe. These projections are useful for preparing general purpose maps showing relief, drainage systems, oceans, wind direction etc.

Many map projections are neither perfectly conformal nor equal area, but represent a compromise between the two. This compromise may be desired wither to achieve a map of more all-around usefulness or because the projection has some other very special property that makes its use essential for certain purposes

Taimoor Gondal · #13 Tuesday, January 10, 2012

6. Write short note on following:-
Bonne’s modified Conical Projection

MAP PROJECTION:

A map projection is a systematic representation of the parallels of latitude and the meridians of longitude of the spherical surface of the earth on a plane surface.
In other words, it is a method of representing the parallels and the meridians of the earth on a plane surface. The network of the parallels and the meridians so formed is called a graticule.

On our earth resembles a sphere. Therefore, a globe being spherical in shape represents the earth truly. Thus a globe is a true representation of the earth. In other words, a globe is true map of the earth. Since a map represents a flat surface and a globe a spherical surface, the shape of the network of the parallels and the meridians on a map is always different from that on a globe. There are a number of methods of transferring the parallels and the meridians of a globe on a plane surface, i.e., constructing map projections. The shape of the network of the parallels and meridians drawn by one method differs from that by the other methods. Therefore, there is a great variety of graticules. A variety in the graticules is necessary to meet various specific purposes.

Earth relationships such as shapes, areas of countries and direction of one place from the other, are not maintained on map. A map projection showing the area of a globe correctly will not maintain the shapes and directions of the areas truly. Thus it is not possible to construct a map projection showing the globe truly and there is always some distortion in the shape of the graticules. Being unable to acquire all the qualities of a globe, a map projection can’t be used as a complete substitute for a globe.

CONICAL MAP PROJECTIONS:

The parallel and the meridians of a globe are transferred to a cone placed on the globe in such a way that its vertex is above one of the poles and it touches the globe along a parallel. The parallel along which the cone touches the globe is called a standard parallel. Where the cone is unrolled into a flat surface the conical projection is formed.

The meridians are all straight lines converging to a point, the vertex of the cone, which is beyond the North Pole above the top of the map. They are at their true distance apart along the standard parallel. The parallels are all equidistant circular arcs drawn with the vertex of the cone as the centre. The distance between any two parallels represents the true distance between them on the globe.

PROPERTIES OF CONICAL PROJECTIONS:

Parallels are arcs of circles which are concentric in most of the conical projections.
The central meridian is a straight line.
Other meridians are either straight line or curves.
The distance between the meridians decrease towards the pole.
They can represent only one hemisphere, at a time, northern or southern.
The standard parallel is correct to the scale.

These projections are most suitable for representing middle latitudes.

TYPES OF CONICAL PROJECTIONS:

Simple conical projections with one standard parallel.
Simple conical projection with two standard parallels.
Bonne’s projection.
Polyconic projection
International map projection.

BONNE’S PROJECTION:

It is a modified conical projection with one standard parallel. It was invented by Rigobert Bonne (1727-1795). A French cartographer.

CONSTRUCTION:

In construction it is very similar to the simple conical projection with one standard parallel. The central meridian is drawn straight and is divided truly, and through the points off division the parallels are drawn as concentric circles as in the simple conical, but the meridians are not straight lines joining the vertex of the cone to the points of division of the standard parallel. Instead of this al the parallels are made of the exact lengths of the corresponding parallels on the globe, and divided truly like the standard parallel. Then the meridians are formed by drawing curves through the corresponding points on each parallel.

EXAMPLE:

Radius of the earth = 250,000,000 inches.
Therefore,
Radius (r) of the globe on the scale of 1/200,000,000

= 1 × 250,000,000
200,000,000

= 1.25 inches.

Draw a circle with radius equal to the radius of the globe, i.e., 1.25 inches. This circle represents the globe. Let NS its polar diameter and WE its equatorial diameter intersect each other at right angles at O, the centre of the circle. This projection is a modified simple conical projection with one-standard Parallel. Like the simple conical projection with one standard Parallel, Bonne’s projection has one standard parallel. The parallel running through the centre part of the projection will obviously be a suitable standard parallel. Therefore, we choose 45ºN parallel of latitude as the standard parallel. Let radius OP make and angle of 45º with OE. Also draw radii Or, Os, Ot and Ou making angles of 15º, 30º, 60º, 75º respectively with OE.

We are required to draw meridians at an interval of 15º.

The length of the arc subtended by 15º = 2Пr × 1/360 × 15

= 2 × 22/7 × 1.25 × 15/360 inch.

= 0.328 inch.

With O as center and radius equal to 0.328 inch draw an arc a b c d e and f drop perpendiculars b l, c k, d j, e i and f h on ON.

Draw perpendiculars to PO. Produce ON to meet PQ at Q. draws a line LM. This line represents the central meridians. With L as centre and QP as radius draw an arc intersecting LM at N’. This arc will describe the standard parallel i.e. 45º N parallel.

To draw the parallels we have to find out the distance between the successive parallels. This distance is equal to the length of the arc subtended by the parallel interval which is 15º in this example.

Therefore,
The length of the arc subtended by 15º

= 2Пr × 1/360 × 15

= 2 × 22/7 × 1.25 × 15/360 inch.

= 0.328 inch

From the point N’, mark off distance N’w, wx and x 90º towards L and distances N’y, y z and z M towards M, each distance being equal to the arc subtended by 15º, i.e., 0.328 inch. With L as centre, draw arcs passing through the points x, w, y, z and M the equator.

Now a O, b l, c k, d j, e I and f h represent the spacing between the meridians along the equator, 15º, 30º, 45º, 60º and 75º parallels respectively. Since the area is bounded by 75º W and 75º E meridians and the meridians interval is 15º, we need to draw 75/15, i.e., 5 meridians to the west of the central meridian (Oº) and 75/15, i.e. 5 meridians to the east of the central meridian. Starting outwards from the central meridian mark off distances along the equator, each distance being equal to a O. similarly mark off distances b l, c k, d j, e I and f h along 15º, 30º, 45º, 60º and 75º parallels respectively. Join the points of divisions on the parallels by smooth curves and let these curves also pass through the pole and the points of divisions on the equator. The curves represent the meridians.
If the meridian interval been 25º instead of 15º in the above projection, the radius of the arc a b c d e f g in fig should have been equal to

= 2 × 22/7 × 1.25 × 25/360 inch.

= 0.545 inch.

PROPERTIES:

The parallels are concentric arcs of circles. The pole is represented as a point on this projection.

All the parallels are correctly divided for spacing the meridians. The scale along all the parallels is, thus, correct.

The central meridian is a straight line and it is correctly divided for spacing the parallels. The scale along the central meridian is, thus, correct. Other meridians being curves are longer than the corresponding meridians on the globe. The scale along them is, thus enlarged. The scale along the meridians increases away from the central meridian.

The central meridian intersects all parallels at right angles. Other meridians intersect the standard parallel at right angles but all other parallels obliquely. The shapes are, therefore, preserved along the central meridians and the standard parallel only. Elsewhere they are distorted, the distortion increasing towards the margins of the projection. The angles which the meridians make with the parallels get less and less than right angles as they diverge away from the central meridians. This projection is, therefore, not orthomorphic.

The scale along the parallels is correct and the distance (perpendiculars) between them is also correct. Evidently, the area between any two parallels on this projection is equal to the area between the same two parallels on the globe. As all the parallels are correct to scale and the perpendicular distance between them is also correct it is, therefore, an area-equal projection.

The rectangle, enclosed by any two parallels and meridians on the globe, is represented in the projection by a parallelogram which is on equal base and of equal height to scale.

LIMITATIONS:

The shapes away from the central meridians are distorted, the distortion increasing away from the central meridians. The shapes in the margins of the projection showing a large area such as Asia are much distorted. Therefore, this projection maintains shapes satisfactorily along with its equal-area property if areas are small and compact and have not large longitudinal extent.

USES:

This projection is most common in atlases

Since it is an equal-area projection and since shapes are maintained satisfactorily for small areas, this projection is commonly used for showing maps of European countries such as Spain, France, and Germany. Etc. it can be used for drawing general-purpose maps.

Large areas such a North America and Australia are also shown on this projection in some atlases.

This projection is also used by small countries of middle latitude for making topographical sheets.

Taimoor Gondal · #14 Tuesday, January 10, 2012

Write short notes on following
c. Uses and limitations of Mercator’s Projection

MAP PROJECTION:

A map projection is a systematic representation of the parallels of latitude and the meridians of longitude of the spherical surface of the earth on a plane surface.
In other words, it is a method of representing the parallels and the meridians of the earth on a plane surface. The network of the parallels and the meridians so formed is called a graticule.

On our earth resembles a sphere. Therefore, a globe being spherical in shape represents the earth truly. Thus a globe is a true representation of the earth. In other words, a globe is true map of the earth. Since a map represents a flat surface and a globe a spherical surface, the shape of the network of the parallels and the meridians on a map is always different from that on a globe. There are a number of methods of transferring the parallels and the meridians of a globe on a plane surface, i.e., constructing map projections. The shape of the network of the parallels and meridians drawn by one method differs from that by the other methods. Therefore, there is a great variety of graticules. A variety in the graticules is necessary to meet various specific purposes.

Earth relationships such as shapes, areas of countries and direction of one place from the other, are not maintained on map. A map projection showing the area of a globe correctly will not maintain the shapes and directions of the areas truly. Thus it is not possible to construct a map projection showing the globe truly and there is always some distortion in the shape of the graticules. Being unable to acquire all the qualities of a globe, a map projection can’t be used as a complete substitute for a globe.

CYLINDRICAL MAP PROJECTION:

In these projections, the parallels and the meridians of the globe are transferred to a cylinder which is a developable surface.

In cylindrical projections we presume that a cylinder surrounds the globe just touching it round the equator or any other great circle (a great circle is a circle the plane of which passes through the centre of the globe. Its plane divides the globe into two equal parts.)
The meridians and the parallels are first transferred to the internal surface of the cylinder and then it is unfolded and developed to form a flat rectangular surface. The network thus obtained is on a cylindrical projection. On this surface:

1. The parallels are straight lines. Each parallel is equal to the length of the equator. Thus, the parallels are longer than the corresponding parallels on the globe.

2. The meridians are straight lines. They intersect the equator at right angles and they are equi-spaced in all latitudes.

3. The length of the equator on the cylinder is equal to the length of the equator on the globe. Therefore, these projections are quite suitable for showing equatorial regions.

In this type the meridians and the parallels are represented by straight lines at right angles to one another. The lengths of the parallels are exaggerated in increasing proportions towards the poles, each parallel being equal to the equator. The distances between any two meridians are thus the same in all latitudes as on the equator. This class of projections is most suitable for maps of the equatorial regions, and so the more useful of them are (non-perspective) equatorial, that is where the cylinder touches the equator. Some of them are also used for maps of the world on a single sheet.

TYPES OF CYLINDRICAL PROJECTIONS:

Following are the main types of cylindrical map projections.

The simple cylindrical projection.
The cylindrical equal-area projection.
The Mercartor’s projection.

MERCATOR’S PROJECTION:

This projection named after its inventor, was devised by Gerardus Mercator, a Dutch, in 1569.

The meridians on the simple cylindrical projection and the cylindrical equal-area projection don not converge towards the poles. They are equi-distant throughout these projections, i.e., the distances between the meridians increases towards the poles in these projections. Mecartor devised a mathematical formula by virtue of which he placed the parallels increasingly father apart towards the poles thereby increasing the lengths of the meridians but taking care that the increase in the lengths of the meridians was in the same proportion in which the lengths of the parallels increased. By doing so he got a true orthomorphic projection. The projection is, therefore, also called the cylindrical orthomorphic projection.

In this projection, as in simple cylindrical projection, the parallels and the meridians are represented by straight lines at right angles to one another, and the meridians are spaced at equal distances. But to preserve the shapes of areas, the distance along the meridians (i.e., between the parallels) are elongated. In various latitudes in proportion to the stretching of the parallels, all of which are represented by exaggerated lengths, all being equal to the equator. In other words, at any latitude the meridians are stretched towards the poles to the same extent as they are done east and west to become parallel to one another. The scale along the meridians is increased in the same proportion as it is done along the parallels, so that it is the same north and south as it is east and west.

CONSTRUCTION:

For a net of the world on this projection, the equator and the meridians are drawn just in the same way as in the simple cylindrical, but the parallels are not drawn at their correct distances apart. The distance between them progressively increase towards the two poles as, to keep correct directions and shapes, the meridians are elongated north and south in the same proportion as they are stretched east and west to be straight lines perpendicular to the equator.

EXAMPLE:

Let us construct a graticule for Mercator’s Projection on the scale of 1:460,000,000 spacing parallels and meridians at 20º interval.

Radius of the earth = 250,000,000 inches.

Therefore,

Radius of the globe on the scale of 1/460, 000, 00

= 1/460,000,000 × 250,000,000

= 0.543 inch.

Length of the equator on the globe = 2Пr (r = radius of the globe)

= 2 × 22/7 × 0.543

= 3.413 inches.

Draw a line AB 3.413 inches long to represent the equator. The equator is a circle on the globe and is subtended by 360º. Since the meridians are to be drawn at an interval of 20º, divide AB into 360/20 or 18 equal parts. Draw lines CAD and FBE perpendicular to AB.

Latitude

Distance of parallel from the equator ( r is the radius of the globe)

10º

0.175 × r

20º

0.356 × r

30º

0.549 × r

40º

0.763 × r

50º

1.011 × r

60º

1.317 × r

70º

1.733 × r

80º

2.436 × r

90º

∞

Now we are required to draw 20º, 40º, 60º, and 80º parallels.

Therefore,

Distance of 20º parallel from the equator = 0.356 × r = 0.365 × 0.543 = 0.193”
Distance of 40º parallel from the equator = 0.763 × r = 0.763 × 0.543 = 0.414”

Distance of 60º parallel from the equator = 1.317 × r = 1.317 × 0.543 = 0.715”

Distance of 80º parallel from the equator = 2.436 × r = 2.436 × 0.543 = 1.325”

Mark off points along the lines AC and BF, the distance of the points from the equator being equal to 0.193”. A line joining these two points will mark 20º N parallel. Again mark off points along the lines AC and BF, keeping the distance of the points from the equator now equal to 0.414”. A line joining these two points will mark 40º N parallel. Similarly draw other parallels.

To draw the meridians, erect perpendiculars on the points of divisions except points A & B on the equator and produce them to so that they meet 80º N and 80º S parallels.

Mark the equator and the central meridians with 0º and parallels and other meridians as shown in the fig.

CDEF is the required graticule.

PROPERTIES:

1. Parallels are meridians are straight lines.

2. The meridians intersect the parallels at right angles.

3. The distance between the parallels go on increasing towards the poles but the distances between the meridians remain the same.

4. All the parallels are of the same length and every one of them is equal to the length of the equator.

5. The length of the equator on this projection is equal to the length of the equator on the globe. Therefore, the scale along the equator is correct. The parallels are longer than the corresponding parallels on the globe.

For example, 30º parallel, 60º parallel and 80º parallel on this projection are 1.154 times, 2.000 times and 5.758 times longer than the corresponding parallels on the globe respectively. The poles cannot be shown on this projection because exaggeration in the scales along 90º parallel and the meridians touching them in infinite.

6. The meridians are longer than the corresponding meridians on the globe. They are made longer so as to make the sale along the meridians at any point equal to the scale along the parallels at the same point. The following three examples illustrate this point:

a. As the length of 1º N parallel is 1.0002 times the length of the 1º N parallel on the globe, the length of the meridians between 0º (equator) and 1º N parallel is 1.0002 times longer than the corresponding meridian on the globe.

b. 20º N parallel on this projection is 1.064 times the length of the 20º N parallel on the globe. Therefore, the length of the meridians between 19º N and 20º N parallels is 1.064 times longer than the corresponding meridians on the globe.

c. 80º N parallel on this projection is 5.758 times the length of the 80º N parallel on the globe. Therefore, the length of the meridian between 79º N and 80º N parallels is 5.758 times longer than the corresponding meridians on the globe.

Thus, the east-west stretching is accompanied by an equal north-south stretching at every point over the entire projection. The actual amount of stretching will vary from one latitude to another. The result of this stretching is that sizes of countries in high latitude are enlarged many times more than their actual sizes. The exaggeration in the sizes of the countries within the tropics is very small. Most of Greenland lies within the polar areas and most of South America within the tropics Greenland which is about one-ninth of the size of South America appears as large as South America on Mercator’s projection.

7. The parallels and meridians also intersect each other at right angles. Therefore, the shape of countries is represented truly at very pint. Since the scale varies from parallel too parallel and is much exaggerated towards the poles, the shape of a large-sized country is distorted; it is larger on the pole ward side and relatively small on the equator ward side. Therefore, shapes of small areas are preserved on this projection but of large countries distorted.

8. At a point, the scale along the meridians is equal to the scale along the parallel. The projection is therefore, orthomorphic.

9. A straight line drawn on this projection makes the same angle with the meridians. A straight line drawn on this projection is, therefore, a line of constant bearing. Such a line is called a loxodrome or a rhumb-line. Thus, compass directions are shown by straight lines and correctly maintained in this projection. Owing to this property, Mercator’s projection is of great value for navigational purposes both on the sea and in the air.

LIMITATIONS:

1. The scale along the parallels and the meridians increases rapidly towards the poles. There being a great exaggeration of scale along the parallels and the meridians in high latitudes, the sizes of the countries on this projection are very large in the polar areas. For this reason, the polar areas cannot be shown satisfactorily on this projection.

2. Poles cannot be shown on this projection because the exaggeration in the scales along the 90º parallel and the meridians touching them is infinite.

USES:

1. This projection is commonly used for navigational purposes both on the sea and the air. The distance along a rhumb-line between any two points is greater than the distance along the great circle between the same two points, on the earth. A rhumb-line on this projection is a straight line but a great circle running more or less in the east-west direction is a curved line. A great circle bends towards the poles—northwards in the northern hemisphere and southwards in the southern hemisphere. A rhumb-line and a great circle, however, run together as a straight line along the equator and the meridians on this projection.

The mariner gets his direction by the rhumb-line but tries to remain as near the great circle as possible to follow the shortest route. Lines indicating the great circles are marked on the maps (drawn on this projection) with the help pf Gonomonic projection. He breaks up the great circle into a number of sections and joins the points of divisions (on the great circles) by lines which serve as various legs of the rhumb-line. The mariner follows the first leg until he reaches the great circle. He then changes his bearing to follow the next leg of the rhumb-line. Thus, he goes on changing his bearings till he reaches his destination.

2. Ocean currents, wind directions and pressure systems are shown on this projection as the directions are maintained truly on this projection.

3. Maps of tropical countries are shown on this projection when they are to be used for general purposes. The reason is that exaggeration in the size of an area is small within the tropics and the shapes of the countries are preserved without much distortion.

Taimoor Gondal · #15 Tuesday, January 10, 2012

Compare the usefulness of Simple Cylindrical, Cylindrical Equal Area and Cylindrical Orthomorphic Projections.

MAP PROJECTION:

A map projection is a systematic representation of the parallels of latitude and the meridians of longitude of the spherical surface of the earth on a plane surface.
In other words, it is a method of representing the parallels and the meridians of the earth on a plane surface. The network of the parallels and the meridians so formed is called a graticule.

On our earth resembles a sphere. Therefore, a globe being spherical in shape represents the earth truly. Thus a globe is a true representation of the earth. In other words, a globe is true map of the earth. Since a map represents a flat surface and a globe a spherical surface, the shape of the network of the parallels and the meridians on a map is always different from that on a globe. There are a number of methods of transferring the parallels and the meridians of a globe on a plane surface, i.e., constructing map projections. The shape of the network of the parallels and meridians drawn by one method differs from that by the other methods. Therefore, there is a great variety of graticules. A variety in the graticules is necessary to meet various specific purposes.

Earth relationships such as shapes, areas of countries and direction of one place from the other, are not maintained on map. A map projection showing the area of a globe correctly will not maintain the shapes and directions of the areas truly. Thus it is not possible to construct a map projection showing the globe truly and there is always some distortion in the shape of the graticules. Being unable to acquire all the qualities of a globe, a map projection can’t be used as a complete substitute for a globe.

CYLINDRICAL MAP PROJECTION:

In these projections, the parallels and the meridians of the globe are transferred to a cylinder which is a developable surface.

In cylindrical projections we presume that a cylinder surrounds the globe just touching it round the equator or any other great circle (a great circle is a circle the plane of which passes through the centre of the globe. Its plane divides the globe into two equal parts.)
The meridians and the parallels are first transferred to the internal surface of the cylinder and then it is unfolded and developed to form a flat rectangular surface. The network thus obtained is on a cylindrical projection. On this surface:

1. The parallels are straight lines. Each parallel is equal to the length of the equator. Thus, the parallels are longer than the corresponding parallels on the globe.

2. The meridians are straight lines. They intersect the equator at right angles and they are equi-spaced in all latitudes.

3. The length of the equator on the cylinder is equal to the length of the equator on the globe. Therefore, these projections are quite suitable for showing equatorial regions.

In this type the meridians and the parallels are represented by straight lines at right angles to one another. The lengths of the parallels are exaggerated in increasing proportions towards the poles, each parallel being equal to the equator. The distances between any two meridians are thus the same in all latitudes as on the equator. This class of projections is most suitable for maps of the equatorial regions, and so the more useful of them are (non-perspective) equatorial, that is where the cylinder touches the equator. Some of them are also used for maps of the world on a single sheet.

TYPES OF CYLINDRICAL PROJECTIONS:

Following are the main types of cylindrical map projections.

The simple cylindrical projection.
The cylindrical equal-area projection.
The Mecartor’s projection.

SIMPLE CYLINDRICAL PROJECTION:

This is a very simple projection in which both the parallels and the meridians are represented by straight lines at right angles to one another and are drawn at their true distance apart. They thus form a series of square.

In this projection the distances along the meridians and the equator are correct but those along the parallels are more and more exaggerated towards the poles, which are extended to be of the same length as the equator.

CYLINDRICAL EQUAL-AREA PROJECTION:

The cylindrical equal-area projection is a real projection in the geometrical sense. In it the planes of the parallels are imagines to be extended to meet the circumscribing cylinder which touches the globe along the equator, and so when the cylinder is infolded, the representations of the parallels are straight lines which are parallel to the equator, and are close together towards the poles. The meridians are also straight lines at right angles to the parallels and are spaced at equal distances, as in the simple cylindrical.

In this projection the scale along the meridians decreases rapidly north and south, as the distance between the parallels are of the same length throughout, though their real lengths diminish to zero at the poles. Therefore, on account of the inequality of scales, along the meridians of the parallel, the shapes are distorted and the projection is far from being orthomorphic. it is however, equal-area, as the area of a zone of a sphere is equal to that of the zone of the cylinder of the same height. Every zone of the projection thus represents the corresponding zone of the sphere in area.

CYLINDRICAL ORTHOMORPHIC OR MERCATOR’S PROJECTION:

This projection named after its inventor, was devised by Gerardus Mercator, a Dutch, in 1569.

The meridians on the simple cylindrical projection and the cylindrical equal-area projection don not converge towards the poles. They are equi-distant throughout these projections, i.e., the distances between the meridians increases towards the poles in these projections. Mercator devised a mathematical formula by virtue of which he placed the parallels increasingly father apart towards the poles thereby increasing the lengths of the meridians but taking care that the increase in the lengths of the meridians was in the same proportion in which the lengths of the parallels increased. By doing so he got a true orthomorphic projection. The projection is, therefore, also called the cylindrical orthomorphic projection.

In this projection, as in simple cylindrical projection, the parallels and the meridians are represented by straight lines at right angles to one another, and the meridians are spaced at equal distances. But to preserve the shapes of areas, the distance along the meridians (i.e., between the parallels) are elongated. In various latitudes in proportion to the stretching of the parallels, all of which are represented by exaggerated lengths, all being equal to the equator. In other words, at any latitude the meridians are stretched towards the poles to the same extent as they are done east and west to become parallel to one another. The scale along the meridians is increased in the same proportion as it is done along the parallels, so that it is the same north and south as it is east and west.

.

COMPARISON BETWEEN THE USEFULNESS OF THE CYLINDRICAL PROJECTIONS:

Cylindrical map projections are suitable for showing the equatorial regions.

In simple cylindrical projection as scale along the meridians are correct. Therefore, a narrow strip of land running in the north-south direction and crossing the equator is shown fairly correctly on this projection while equal area projection is used for showing tropical countries. Similarly maps of tropical countries are shown on Mercator’s projection when they are to be used for general purposes. The reason is that exaggeration in the size of an area is small within the tropic and the shapes of the countries are preserved without much distortion.

In simple cylindrical projection, a narrow belt along the equator can be shown fairly correctly on this projection. Since it is neither equal area nor orthomorphic, maps on this projection are used for general purposes only. This projection can be used for showing a railway or a road connecting Cairo (Egypt) with Durban (Republic of South Africa) because both of these towns are located near 31º E meridian. Being an equal-area, cylindrical equal area projection is drawn mainly for showing the world distribution of tropical products such as rubber, coconut, rice, cotton, groundnut, etc. besides the maps of the equatorial regions, world maps are also frequently drawn upon it. Mercator’s projection is commonly used for navigational purposes both on the sea and the air. It is used in flying maps in air navigation and in variety of world maps. Ocean currents, wind directions and pressure systems are shown on this projection as the directions are maintained truly on this projection.

The distance along a rhumb-line between any two points is greater than the distance along the great circle between the same two points, on the earth. A rhumb-line on this projection is a straight line but a great circle running more or less in the east-west direction is a curved line. A great circle bends towards the poles—northwards in the northern hemisphere and southwards in the southern hemisphere. A rhumb-line and a great circle, however, run together as a straight line along the equator and the meridians on this projection.

The mariner gets his direction by the rhumb-line but tries to remain as near the great circle as possible to follow the shortest route. Lines indicating the great circles are marked on the maps (drawn on this projection) with the help pf Gnomonic projection. He breaks up the great circle into a number of sections and joins the points of divisions (on the great circles) by lines which serve as various legs of the rhumb-line. The mariner follows the first leg until he reaches the great circle. He then changes his bearing to follow the next leg of the rhumb-line. Thus, he goes on changing his bearings till he reaches his destination
.
When simple cylindrical projection is made transverse so that the cylinder touches the central meridians of a country instead of the equator, it becomes a useful projection known as Cassini’s. . It is used for one-inch-to-a- mile maps of England and six-inch-to-a-mile maps of the British Isles .When Mercator’s projection is made transverse, with the central meridians of a country used as the equator, it is called the Gauss Conformal. It is used for maps of the countries lying north and couth like Egypt.

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